Recently, Chern insulators in an antiferromagnetic (AFM) phase have been suggested theoretically and predicted in a few materials. However, the experimental observation of two-dimensional (2D) AFM quantum anomalous Hall effect is still a challenge to date. In this work, we propose that an AFM Chern insulator can be realized in a 2D monolayer of NiOsCl6 modulated by a compressive strain. Strain modulation is accessible experimentally and used widely in predicting and tuning topological nontrivial phases. With first-principles calculations, we have investigated the structural, magnetic, and electronic properties of NiOsCl6. Its stability has been confirmed through molecular dynamical simulations, elasticity constant, and phonon spectrum. It has a collinear AFM order, with opposite magnetic moments of 1.3 mu B on each Ni/Os atom, respectively, and the N & eacute;el temperature is estimated to be 93 K. In the absence of strain, it functions as an AFM insulator with a direct gap with spin-orbital coupling included. Compressive strain will induce a transition from a normal insulator to a Chern insulator characterized by a Chern number C = 1, with a band gap of about 30 meV. This transition is accompanied by a structural distortion. Remarkably, the Chern insulator phase persists within the 3%-10% compressive strain range, offering an alternative platform for the utilization of AFM materials in spintronic devices.